Determining position of a node and representing the position as a position probability space

ABSTRACT

Methods and apparatus are provided for determining and representing a location or position of a node in a network. When the node receives position measurement information from a reference node, the node generates, based on the position measurement information, a position probability space (PPS) which defines a space that encompasses possible positions where the node is possibly positioned in the network. The PPS includes a centroid (i.e., a set of coordinates), and a set of vectors which originate from the centroid and define the space around the centroid. The magnitude of each vector reflects the accuracy of the position in the direction of the vector.

FIELD OF THE INVENTION

The present invention relates generally to locationing or positioningtechniques in wireless communication networks, and in particular todetermining and representing a location or position of a node within awireless communication network.

BACKGROUND

Wireless communication networks can generally be classified as eitherinfrastructure-based wireless networks or ad hoc wireless networks.

An infrastructure-based wireless network typically includes acommunication network with fixed and wired gateways. Manyinfrastructure-based wireless networks employ a mobile unit or hostwhich communicates with a fixed base station that is coupled to a wirednetwork. The mobile unit can move geographically while it iscommunicating over a wireless link to the base station. When the mobileunit moves out of range of one base station, it may connect or“handover” to a new base station and starts communicating with the wirednetwork through the new base station.

In comparison to infrastructure-based wireless networks, such ascellular networks or satellite networks, ad hoc networks areself-forming networks which can operate in the absence of any fixedinfrastructure, and in some cases the ad hoc network is formed entirelyof mobile nodes. An ad hoc network typically includes a number ofgeographically-distributed, potentially mobile units, sometimes referredto as “nodes,” which are wirelessly connected to each other by one ormore links (e.g., radio frequency communication channels). The nodes cancommunicate with each other over a wireless media without the support ofan infrastructure-based or wired network. Links or connections betweenthese nodes can change dynamically in an arbitrary manner as existingnodes move within the ad hoc network, as new nodes join or enter the adhoc network, or as existing nodes leave or exit the ad hoc network.

In many wireless communication networks, it is desirable to determinethe location or position of a node within that network. In conventionallocationing or positioning technologies, a location or position of anode is typically represented by a point (i.e., a set of coordinates)and a simple indication of the accuracy or precision of that position.For instance, the location or position of the node can be representedusing a circle of radius (r) that originates from a point (x,y), wherethe radius (r) of the circle represents the accuracy or precision ofthat position.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying figures, where like reference numerals refer toidentical or functionally similar elements throughout the separate viewsand which together with the detailed description below are incorporatedin and form part of the specification, serve to further illustratevarious embodiments and to explain various principles and advantages allin accordance with the present invention.

FIG. 1 is a flowchart illustrating a method for determining a positionprobability space (PPS) and re-centering a centroid of the PPS;

FIG. 2 is a flowchart illustrating a method for determining a positionprobability space (PPS) in accordance with some embodiments of thepresent invention;

FIG. 3A is a graph which illustrates an example of a positionprobability space (PPS) for a local node in accordance with someembodiments of the present invention;

FIG. 3B is a diagram illustrating a method for modifying one vector of aPPS of a local node based on position measurement information from areference node in accordance with some embodiments of the presentinvention;

FIG. 3C is a diagram illustrating a method for re-centering a centroid(x,y) of a PPS in accordance with some embodiments of the presentinvention;

FIG. 4 is a graph of an existing position probability space (EPPS) alongwith positioning measurement information from two reference nodes thatare used to re-define the EPPS as an updated local position probabilityspace (UPPS) in accordance with some embodiments of the presentinvention; and

FIG. 5 is a graph of an existing position probability space (EPPS)displayed along with a reference position probability space (RPPS)associated with a single mobile reference node that is used tore-compute or re-define the EPPS as an updated local positionprobability space (UPPS) in accordance with some other embodiments ofthe present invention.

Skilled artisans will appreciate that elements in the figures areillustrated for simplicity and clarity and have not necessarily beendrawn to scale. For example, the dimensions of some of the elements inthe figures may be exaggerated relative to other elements to help toimprove understanding of embodiments of the present invention.

DETAILED DESCRIPTION

Methods and apparatus are provided for determining and representing alocation or position of a node in a network. When the node receivesposition measurement information from a reference node, the nodegenerates, based on the position measurement information, a positionprobability space (PPS) which defines a space that encompasses possiblepositions where the node is possibly positioned in the network. The PPSincludes a centroid (i.e., a set of coordinates), and a set of vectorswhich originate from the centroid and define the space around thecentroid. The magnitude of each vector reflects the accuracy of theposition in the direction of the vector.

Before describing in detail embodiments that are in accordance with thepresent invention, it should be observed that the embodiments resideprimarily in combinations of method steps and apparatus componentsrelated to determining and representing a location or position of anode. Accordingly, the apparatus components and method steps have beenrepresented where appropriate by conventional symbols in the drawings,showing only those specific details that are pertinent to understandingthe embodiments of the present invention so as not to obscure thedisclosure with details that will be readily apparent to those ofordinary skill in the art having the benefit of the description herein.

In this document, relational terms such as first and second, top andbottom, and the like may be used solely to distinguish one module oraction from another module or action without necessarily requiring orimplying any actual such relationship or order between such modules oractions. The terms “comprises,” “comprising,” or any other variationthereof, are intended to cover a non-exclusive inclusion, such that aprocess, method, article, or apparatus that comprises a list of elementsdoes not include only those elements but may include other elements notexpressly listed or inherent to such process, method, article, orapparatus. An element proceeded by “comprises . . . a” does not, withoutmore constraints, preclude the existence of additional identicalelements in the process, method, article, or apparatus that comprisesthe element.

It will be appreciated that embodiments of the invention describedherein may be comprised of one or more conventional processors andunique stored program instructions that control the one or moreprocessors to implement, in conjunction with certain non-processorcircuits, some, most, or all of the functions for determining andrepresenting a location or position of a node described herein. Thenon-processor circuits may include, but are not limited to, a radioreceiver, a radio transmitter, signal drivers, clock circuits, powersource circuits, and user input devices. As such, these functions may beinterpreted as steps of a method for determining and representing alocation or position of a node. Alternatively, some or all functionscould be implemented by a state machine that has no stored programinstructions, or in one or more application specific integrated circuits(ASICs), in which each function or some combinations of certain of thefunctions are implemented as custom logic. Of course, a combination ofthe two approaches could be used. Thus, methods and means for thesefunctions have been described herein. Further, it is expected that oneof ordinary skill, notwithstanding possibly significant effort and manydesign choices motivated by, for example, available time, currenttechnology, and economic considerations, when guided by the concepts andprinciples disclosed herein will be readily capable of generating suchsoftware instructions and programs and ICs with minimal experimentation.

Overview

There are numerous techniques and technologies which can be utilized todetermine and represent a location or position of a node. In most, ifnot all, of the these technologies, the location or position of the nodeis communicated to an end user as a set of coordinates (e.g., x,y orx,y,z) with some indication of the precision (e.g., a circle having aradius (r) centered at those coordinates). In many environments,representing the location or position of a node in a network usingabsolute coordinates and a simple indication of precision is notnecessarily the optimum approach.

Positioning measurements provided in conventional positioningtechnologies can be used to determine where a node is not located (i.e.,positioning measurements can allow a node to determine positions whereit can not possibly be located), but can not be used to determineprecisely where a node is located. Oftentimes the location or positionof the node is only known with a low degree of precision, and displayinga position using absolute coordinates does not allow an end user todetermine where the location or position is likely to be. For example,when position of a node is displayed as a circle, the end user is unableto reconcile the displayed position with the actual real world positionsince there is no way for the end user to determine the precision of thelocation or position or where the errors in this precision lie or whatthe values of those errors are, etc. Moreover, in some cases, the enduser may want to know the location or position of the node with more orless accuracy. As such, in many cases, the known techniques forrepresenting the location or position of a node are insufficient, and itwould be desirable to provide the end user with a way to also estimateof the precision of the location or position.

Moreover, representing the location or position of the node using only acentroid and some indication of precision allows only for symmetricalpositioning errors to be communicated to the end user, when in reality,positioning errors are rarely symmetrical. Environmental conditions, forinstance, are rarely symmetrical and therefore the precision of positionmeasurement information can be different depending on the direction (orangle) one is considering. This is particularly true when the locationor position of the node is calculated based on different types ofposition measurement information from different reference nodes sincethe relative precision of the different types of position measurementinformation from the different reference nodes can vary. Unfortunately,in many environments, this position measurement information can beextremely inaccurate.

The disclosed embodiments relate to techniques for determining andrepresenting a location or position of a node in a communicationnetwork. The disclosed embodiments can be used in conjunction with anyknown locationing or positioning technology that relies on positionmeasurement information which does not have uniform precision. Thedisclosed techniques can allow for the location or position of a node tobe determined based on position measurement information from differentreference nodes even when the precision of the different positionmeasurement information varies or is of “differing precision.”

Embodiments of the present invention represent the position of a nodeusing a position probability space (PPS). As used herein the term“position probability space (PPS)” refers to a zone or space where anode is likely to be located or positioned. The location or position ofthe node, and the precision of this location or position, arerepresented as a centroid (i.e., a set of coordinates) with a zone orspace around it which reflects a region where the node is likely to belocated with relative certainty or precision. A contour of the zone orspace around the centroid is defined by a series of vectors (magnitudesand angles) which originate from the centroid. The PPS represents notonly the location or the position of the node, but also the accuracy orprecision of that location or position. Thus, in the disclosedembodiments, instead of representing the location or position of thenode as a point, the location or position of the node is displayed as anarea or volume, which is typically asymmetric, to help illustrate thelocation or position of the node to the end user taking into account thediffering precisions of the position measurement information.

Depending on the implementation, the PPS can represent the location orposition of the node within a known area where the node is likely to belocated or a known volume where the node is likely to be located. Byrepresenting the location or position of a node using a PPS, thelocation or position of the node can be expressed as a known area or avolume of probability or precision instead of as a point. For example,in some implementations, the PPS represents the location or position ofthe node as an area or “in two-dimensional space,” and this area can beexpressed as a parametric function representing a discretized view of aplane. By contrast, in other implementations, the PPS represents thelocation or position of the node as a volume or “in three-dimensionalspace,” and this volume can be represented as a matrix of valuesrepresenting a discretized view of a space.

A PPS representation of a node's location or position is more accuratethan a center/radius representation and allows for much highergranularity. A PPS representation of a node's location or position isalso easy to display on a graphical interface and “speaks” to the usermore than a grid or a circle. Using a PPS to represent the location orposition of the node can be particularly useful in environments wherethe precision of position measurement information tends to vary (e.g.,in indoor position calculation scenarios to display a location ofwide-band radios where small errors in position may indicate differentfloors, rooms, or buildings).

FIG. 1 is a flowchart illustrating a method 100 for determining aposition probability space (PPS) and re-centering a centroid of the PPS.As used herein, the terms “local node” and “reference node” or“reference nodes” will be used to differentiate between a local nodethat is determining its position probability space (PPS), and one ormore reference nodes that are providing position measurement informationto the local node so that the local node can re-compute or refine itsPPS.

The first time method 100 starts, the local node may have some type ofposition information, for example, a global positioning system (GPS)measurement, position information from a reference node, user input orprior position information that the local node has previously calculatedand stored in memory. The local node can use this position informationto calculate a representation of its position referred to here as astarting position estimate. If no prior position information isavailable, then the local node assumes that it has a starting positionestimate which consists of a point and a set of vectors having infinitemagnitudes.

At step 105, the first time the method 100 executes or iterates, thelocal node determines its initial PPS (IPPS) by performing steps 110 and120. Thereafter, during each subsequent execution or iteration of method100, the method 100 re-computes or redefines its current PPS as anupdated PPS (UPPS).

At step 110, the local node receives and collects positioningmeasurement information from one or more reference nodes. The positionmeasurement information received from a particular reference node canbe, for example, a set of data such as distances to reference points,absolute coordinates or motion parameters. Each set of positionmeasurement information received from a particular reference node has anaccuracy or precision associated therewith which depends on factors suchas clock accuracy, the number of samples, the RF environment or thesampling rate.

At step 120, the local node uses the starting position estimate and thepositioning measurement information to generate or create an initial PPS(IPPS). A PPS and techniques for generating it are described below withrespect to FIG. 2 and 3B, respectively. As noted above, the local nodegenerates and stores the IPPS as a centroid (defined by coordinateseither x, y or x, y, z) and a series of vectors originating at thecentroid to define the space, where each vector is specified as amagnitude and an angle/direction. In this regard, the “space” can beeither an area or a volume depending on the implementation. The spacerepresents a zone of probability where the local node is located.Although not illustrated in the method 100 of FIG. 1, in someimplementations, a different series of vectors can be determined foreach level of accuracy/precision desired, and in such implementations aseries of IPPSs can be generated with each one having its own accuracyor precision.

Steps 150 and 160 are optional and therefore illustrated in dotted lineboxes. At step 150, the local node determines whether the centroid ofthe PPS is substantially centered within the space or zone that definesthe PPS. In some cases, the centroid of the PPS can be off-center inwhich case it becomes important to re-center the centroid of the PPS sothat the PPS representation of the location or position of the node iscloser to the shape of a circle (in a two-dimensional representation) ora sphere (in a three-dimensional representation).

When the local node determines that the centroid of the PPS issubstantially centered within the space or zone defined by the PPS, themethod 100 proceeds to step 155, where the IPPS is stored and/orcommunicated and/or displayed by the local node to the end user so thatthe PSS may then be viewed by the end user. The end user can be either aprovider or a consumer of position and distance measurements. The IPSSmay be relayed to the end user without modification, or the centroid andvectors which represent the IPSS may first be converted to some otherrepresentation (zone, grid, polygon etc.).

On the other hand, when the local node determines that the centroid ofthe PPS is not substantially centered within the space or zone definedby the PPS, the method 100 proceeds to step 160, where the centroid ofthe IPPS is re-centered. In other words, when the local node determinesthat the centroid of the IPPS is not substantially centered within thecontour that defines the IPPS, then the method 100 proceeds to step 160,where the local node performs calculations to re-center the centroid ofthe IPPS such that it is substantially centered within the contour thatdefines the IPPS. Techniques for re-calculating the centroid of thepolygon having a contour defined by the vectors (angles and precisions)are known in the art and therefore are not described in detail herein.An example illustration of re-centering the centroid (x,y) of a PPS 301is illustrated in FIG. 3C. The method 100 then proceeds to step 155where the re-centered IPPS is stored and/or communicated and/ordisplayed to the end user (e.g., the local node communicates and/ordisplays the re-centered IPPS to the end user).

Following step 155, the method 100 loops back to step 105. Each time themethod 100 executes or iterates the local node will determine an updatedPPS (UPPS). In other words, the definition of the PPS that was computedduring the most recent iteration of method 100 is refined by shorteningor reducing the magnitudes or “lengths” of the vectors which define theprior PPS based on new or updated positioning measurement informationfrom one or more reference nodes. In this manner, the overall space orzone represented by by the UPPS is reduced in comparison to the priorPPS and the zone of probability where the local node is positionedbecomes more accurate with each iteration of method 100. As time goesby, the magnitude of the vectors may increase because the local node maybe moving and the measurement data may become obsolete.

Generating a Position Probability Space (PPS)

FIG. 2 is a flowchart illustrating a method 220 for determining aposition probability space (PPS) in accordance with some embodiments ofthe present invention.

The method 220 begins at step 222, where the local node selects a vectorof its starting position estimate or an existing PPS. During the firstiteration of method 220, the local node will select the “first” vectorof either the starting position estimate or the existing PPS dependingon what iteration the method 100 of FIG. 1 is presently in. For example,during the first iteration of method 100 of FIG. 1, the local node doesnot yet have a PPS, but must instead uses its starting position estimateto determine an IPPS. During a subsequent iteration of method 100 ofFIG. 1, the local node uses the IPPS to determine an updated PPS (UPPS),and so on. For purposes of discussion, the remaining description of FIG.2 will refer to vectors of an existing PPS, although the same principlesapply to vectors of a starting position estimate as well.

At step 224, the local node determines whether the currently selectedvector of the PPS intersects a circle which is defined based on positionmeasurement information from a reference node. The circle is centered atthe location of the reference node and has a radius equal to thedistance between the local node and the reference node.

When the local node determines that the currently selected vector of thePPS does not intersect the circle associated with the reference node,the method 220 loops back to step 222, where the local node selects thenext vector of the PPS.

When the local node determines that the currently selected vector of thePPS does intersect the circle associated with the reference node, themethod 220 proceeds to step 226, where the local node determines whetherthe distance between the centroid of the PPS and the intersection pointof the currently selected vector is less than the current magnitude ofthe selected vector.

When the local node determines that the distance between the centroid ofthe PPS and the intersection point of the currently selected vector isnot less than (i.e., is greater than or equal to) the current magnitudeof the selected vector, the method 220 loops back to step 222, where thelocal node selects the next vector of the PPS. By contrast, when thelocal node determines that the distance between the centroid of the PPSand the intersection point of the currently selected vector is less thanthe current magnitude of the selected vector, then method 220 proceedsto step 228, where the local node reduces the magnitude (or length) ofthe currently selected vector to the distance between the centroid ofthe PPS and the intersection point of the currently selected vector. Themethod 220 then proceeds to step 230, where the local node determinewhether the currently selected vector is the last vector of the PPS.When the local node determines that the currently selected vector is notthe last vector of the PPS, then method 220 loops back to step 222. Whenthe local node determines that the currently selected vector is the lastvector of the PPS, then method 220 proceeds to step 150 of FIG. 1.

Numerical Representation of a Two-Dimensional Position Probability Space(PPS)

FIG. 3A is a graph 320 which illustrates an example of a positionprobability space (PPS) 302 for a local node in accordance with someembodiments of the present invention. In this example, the PPS 302 isdisplayed in a two-dimensional polar coordinate system as a parametricfunction that defines the expected position of a node as a geographicalarea, and therefore the PPS 302 is actually a position probability area(PPA), but will be referred to as a PPS for purposes of consistency. ThePPS 302 includes a centroid (x, y) and a contour 302 having multiple,different radii all of which originate at the centroid (x, y). Theseradii can be initially defined by series of vectors 304, 306, 308, 310,312, 314, 316, 318 which define the contour 302 of a two-dimensionalspace which defines the PPS 300.

The graph 320 of the PPS 302 represents the probable position of thelocal node as a centroid (x, y) and a series of vectors 304-318represented by single headed arrows which originate from the centroid(x, y). In this example, the number (N) of vectors used to represent thePPS 302 is eight (8), and the vectors 304-318 have angles (0, π/8, π/4,3π/8, π/2, 5π/8, 3π/4, 7π/8) corresponding to an angular resolution ofπ/8, and corresponding magnitudes (d₀ through d₈). However, the number(N) of vectors can be adjusted to accommodate a need for higher or lowerprecision, as illustrated in Table 1 which is a parametricrepresentation of a PPS 302, where the first row is a series of angles(0 . . . 2π(N−1)/N), and the second row is a series of correspondingmagnitudes (d₀ through d_(N−1)).

TABLE 1 Angle (°) 0 2π/N 4π/N 6π/N . . . 2π (N − 1)/N Distance (m) d₀ d₁d₂ d₃ . . . d_(N−1)

In this example, the vector 304 has a length/magnitude (d₀) thatreflects the precision of position measurement information for aparticular angle of the vector 304 (0 degrees). The local node can belocated at any point within the contour of the PPS 302, but can not belocated or positioned at points outside the contour of the PPS 302.

While the PPS 302 described with reference to FIG. 3A is representedusing only two dimensions, in alternative implementations, the centroidand the set of angles can be described in three dimensions as aprobability volume or zone. In such implementations, in addition tolongitude and latitude, the centroid is defined with altitude, and theset of angles would be representable in a matrix instead of an array.

To illustrate how the method 220 of FIG. 2 would apply in a practicalexample, steps 222-228 of FIG. 2 will be described with reference toFIG. 3B. FIG. 3B is a diagram illustrating a method for shortening avector 310 of an existing PPS 302 of a local node 300 based on positionmeasurement information 332 from a reference node 331 in accordance withsome embodiments of the present invention.

In FIG. 3B, the first vector of PPS 302 that is selected is vector 304.In the example illustrated in FIG. 3B, the circle 332 is centered at thelocation of the reference node 331 and has a radius (r) equal to thedistance between the local node 300 and the reference node 331, andthere is no intersection between vector 304 and circle 332. In theexample illustrated in FIG. 3A, step 222 and 224 would continue toiterate and loop back until the selected vector is vector 308, and whenthe method 300 reaches step 224, the local node will determine thatvector 308 does intersect the circle 332, and then proceeds to step 226.At step 226, the local node will determine that the distance between thecentroid of the PPS and the intersection point of the currently selectedvector 308 is not less than the current magnitude of the selected vector308, but is instead of equal magnitude (i.e., vector 308 stops preciselyon circle 332), and therefore the method 300 will loop back to step 222,where vector 310 is selected as the next vector. When vector 310 is thecurrently selected vector, the method will proceed from step 222 to step224 to step 226, where the local node will determine that the distancebetween the centroid of the PPS and the intersection point of thecurrently selected vector 310 is less than the current magnitude of theselected vector 310, and the method would then proceed to step 228. Atstep 228, the local node reduces the magnitude (or length) of thecurrently selected vector 310 to the distance between the centroid ofthe PPS 302 and the intersection point of the currently selected vector310. The new magnitude of the currently selected vector 310 is now 310′.

FIG. 3C is a diagram which illustrates re-centering of a centroid (x,y)of a PPS 302 in accordance with some embodiments of the presentinvention. As described above with reference to steps 150 and 160 ofFIG. 1, when the local node determines that the centroid (x, y) of thePPS 302 is not substantially centered within the contour that definesthe PPS 302, then the local node performs calculations to re-center thecentroid (x1, y1) of the PPS 302′ such that it is substantially centeredwithin the contour that defines the PPS 302′. Techniques forre-calculating the centroid of the polygon having a contour defined bythe vectors and angles are well-known in the art and therefore will notbe described in detail herein.

In the scenarios above, techniques are described for determining aninitial position probability space (IPPS), re-centering a centroid ofthe IPPS, and continuously re-computing an updated position probabilityspace (UPPS) as position measurement information is received fromreference nodes by a local node. In some cases, the location or positionof reference nodes are fixed and hence known. Techniques will bedescribed herein below for computing a UPPS when the local node has anexisting PPS for the local node (e.g., the IPPS) and the locations orpositions of the reference nodes are known.

FIG. 4 is a graph of an existing position probability space (EPPS) 422displayed in polar coordinate system along with positioning measurementinformation 432, 434 from two reference nodes 431, 433 that is used tore-define the EPPS 422 as an updated local position probability space(UPPS) 452 in accordance with some embodiments of the present invention.

Here, the EPPS 422 includes a centroid (not labeled) and a series ofvectors which originate at the centroid. The EPPS 422 defines a contourof a two-dimensional space where the local node can potentially belocated. The node can be located at any point inside or within thecontour of the EPPS 422. All points outside the EPPS 422 are eliminatedfrom consideration since it is not possible for the local node to be inthose locations/positions.

Because the reference nodes 431, 433 have a known location or position,the position of the reference nodes is relatively predictable, and cantherefore be represented using a simple circle. The positioningmeasurement information provided to the local node from the referencenode 431 defines a radius of dotted-line circle 432, and positioningmeasurement information provided to the local node from the referencenode 433 defines a radius of dotted-line circle 434.

The local node can use position measurement information 431, 432received from the reference nodes 431, 432 to compute an updated PPS byshortening vectors of the EPPS 422 based on position measurementinformation 431, 432. In this implementation, the local node candetermine which portions of the EPPS 422 overlap with circles 432, 434,and the resultant overlapping area represents the UPPS 452. In otherwords, the superposition of the EPPS 422 and circles 432, 434 definesthe UPPS 452. The local node can be anywhere within the UPPS 452, andhence the position of the local node is specified with a much higherdegree of precision since the UPPS 452 has a smaller area than the EPPS422.

In the scenarios discussed herein above, techniques are described fordetermining an initial position probability space (IPPS), re-centering acentroid of the IPPS, and continuously re-computing an updated positionprobability space (UPPS) as position measurement information is receivedfrom reference nodes by a local node. Techniques are also described forcomputing a UPPS when the local node has an IPPS and the locations orpositions of the reference nodes are known. In other cases, a referencenode can be mobile and therefore the location or position of thereference node is unknown (or known only with some degree of accuracy orprecision). Techniques will be described herein below with reference toFIG. 5 for computing a UPPS when the local node has an IPPS and thelocation or position of the reference node is known only with a limitedcertainty based on a reference position probability area (RPPA)associated with the reference node.

FIG. 5 is a graph of an existing position probability space (EPPS) 522displayed in polar coordinate system along with a reference positionprobability space (RPPS) 531 associated with a single mobile referencenode that is used to re-compute or re-define the EPPS 522 as an updatedlocal position probability space (UPPS) 552 in accordance with someembodiments of the present invention.

The EPPS 522 of the local node represents the probable position of thelocal node as a centroid (x, y) and a series of vectors represented bysingle headed arrows which originate from the centroid (x, y). The EPPS522 defines a contour of a two-dimensional space where the local nodecan potentially be located. The local node can be located at any pointinside or within the contour of the EPPS 522. All points outside theEPPS 522 are eliminated from consideration since it is not possible forthe local node to be in those locations/positions.

Because the reference node does not have a well-known position (e.g., itis not fixed), the position of the reference node are represented usinga RPPS 531 that is determined by the reference node using the techniquesdescribed above. The RPPS 531 of the reference node represents theprobable position of the reference node as a centroid (x_(Ref), y_(Ref))and a series of vectors 532A-546A represented by single headed arrowswhich originate from the centroid (x_(Ref), y_(Ref)). In FIG. 5, thepositioning measurement information 532, 534, 536, 538, 540, 542, 544,546 from the mobile reference node is illustrated as a group of circles,and the each of the circles 532, 534, 536, 538, 540, 542, 544, 546 iscentered at (i.e., has a radius that originates at) the end of thevector having the same reference numeral. For example, circle 544 has aradius that originates at the end of the vector 544A. The radius ofcircle 544 is equal to the distance between the reference node and thelocal node.

Here the local node computes UPPS 552 (illustrated by the dotted-linecontour) for the local node by shortening vectors of the EPPS 522 basedon position measurement information 532, 534, 536, 538, 540, 542, 544,546 from the RPPS 631 associated with the mobile reference node. In thisimplementation, the local node can compute the UPPS 552 by determiningwhich portions of the existing PPS 522 overlap with each of the circles532, 534, 536, 538, 540, 542, 544, 546 associated with vectors 532A,534A, 536A, 538A, 540A, 542A, 544A, 546A of the RPPS 531, and theresultant overlapping area represents the UPPS 552. In other words,after all of the circles 532, 534, 536, 538, 540, 542, 544, 546 havebeen mapped with respect to the EPPS 522, the UPPS 552 is generated byeliminating all points outside of those circles 532, 534, 536, 538, 540,542, 544, 546 (i.e., any points that are not within at least one of thecircles 532, 534, 536, 538, 540, 542, 544, 546) from the EPPS 522 sinceit is not possible for the local node to be that far away from thereference node, even using the most conservative estimate of thereference node's position. As illustrated in FIG. 5, the superpositionof the EPPS 522 and circles 532, 534, 536, 538, 540, 542, 544, 546associated with vectors 532A, 534A, 536A, 538A, 540A, 542A, 544A, 546Aof the RPPS 531 defines the UPPS 552. In this example, portion of thevectors 524, 526, 528 of the EPPS 522 are eliminated or shortened in theUPPS 552. The local node can be anywhere within the UPPS 552, and hencethe position of the local node is specified with a much higher degree ofprecision since the UPPS 552 has a smaller area than the EPPS 522.

In the foregoing specification, specific embodiments of the presentinvention have been described. However, one of ordinary skill in the artappreciates that various modifications and changes can be made withoutdeparting from the scope of the present invention as set forth in theclaims below. Accordingly, the specification and figures are to beregarded in an illustrative rather than a restrictive sense, and allsuch modifications are intended to be included within the scope ofpresent invention. The benefits, advantages, solutions to problems, andany element(s) that may cause any benefit, advantage, or solution tooccur or become more pronounced are not to be construed as a critical,required, or essential features or elements of any or all the claims.The invention is defined solely by the appended claims including anyamendments made during the pendency of this application and allequivalents of those claims as issued.

1. In a network comprising a node and at least one reference node, amethod comprising: receiving, at the node, position measurementinformation from the reference node; and generating, at the node basedon the position measurement information, a position probability space(PPS) which defines a space that encompasses possible positions wherethe node is possibly positioned in the network.
 2. A method according toclaim 1, wherein the PPS comprises: a centroid comprising a set ofcoordinates; and a set of vectors which originate from the centroid anddefine the space around the centroid, wherein a magnitude of each vectorreflects the accuracy of the position in the direction of the vector. 3.A method according to claim 2, wherein the node has a starting positionestimate comprising a starting centroid and a set of starting vectors,wherein the position measurement information defines a circle centeredat the location of the reference node and has a radius equal to thedistance between the node and the reference node, and wherein the stepof generating, at the node based on the position measurementinformation, a position probability space (PPS), comprises: (a)selecting, at the node, a currently selected vector of the startingposition estimate; (b) determining, at the node, whether the currentlyselected vector intersects the circle; (c) determining, at the node whenthe currently selected vector intersects the circle, a distance betweena starting centroid of the starting position estimate and anintersection point of the currently selected vector; (d) determining, atthe node, whether the distance is less than the magnitude of thecurrently selected vector; (e) reducing the magnitude of the currentlyselected vector, at the node when the distance is less than themagnitude of the currently selected vector, to the distance between thestarting centroid and the intersection point of the currently selectedvector; and (f) repeating steps (a) through (e) for each vector of thestarting position estimate.
 4. A method according to claim 3, furthercomprising: selecting, at the node, a next vector of the startingposition estimate when the node determines that the currently selectedvector of the starting position estimate does not intersect the circleor when the node determines that the distance between the startingcentroid of the starting position estimate and the intersection point ofthe currently selected vector is greater than or equal to the magnitudeof the currently selected vector of the starting position estimate.
 5. Amethod according to claim 2, further comprising: receiving, at the node,updated position measurement information from the reference node; andgenerating, at the node based on the updated position measurementinformation, an updated PPS (UPPS) by reducing the magnitudes of thevectors which define the PPS to reduce a space occupied by the UPPS incomparison to the space occupied by the PPS.
 6. A method according toclaim 2, further comprising: determining, at the node, whether thecentroid of the PPS is substantially centered within the space thatdefines the PPS; and re-centering the centroid of the PPS such that itis substantially centered within the PPS when the node determines thatthe centroid of the PPS is not substantially centered within the spacethat defines the PPS.
 7. A method according to claim 2, wherein thereference nodes comprise a first reference node having a first fixedlocation and a second reference node having a second fixed location, andfurther comprising: receiving, at the node, first position measurementinformation from the first reference node, where the first positionmeasurement information is represented as first space centered at thefirst fixed location and having a first radius; receiving, at the node,second position measurement information from the second reference node,where the second position measurement information is represented as asecond space centered at the second fixed location and having a secondradius, wherein precision of the first position measurement informationdiffers from precision of the second position measurement information;determining, at the node, which portions of the PPS overlap with boththe first and second spaces; and generating, at the node, an updatedposition probability space (UPPS) for the node by removing portions ofany vectors of the PPS that do not overlap with both the first space andthe second space such that the UPPS is defined by the overlappingportions of the PPS, the first space and the second space.
 8. A methodaccording to claim 2, wherein one of the reference nodes comprises amobile reference node having a location specified by a referenceposition probability space (RPPS) associated with the mobile referencenode, and further comprising: receiving, at the node, the RPPS, whereinthe RPPS comprises a reference centroid and a set of reference vectorsassociated with the mobile reference node, wherein each of the referencevectors defines a reference space, wherein each reference spacecomprises a reference centroid that is centered at the end of thereference vector and has a reference radius that originates from thereference centroid; determining, at the node, which portions of the PPSoverlap with each of the reference spaces of the RPPS; and generating,at the node, an updated position probability space (UPPS) for the nodeby removing portions of any vectors of the PPS that do not overlap withat least one of reference spaces such that the UPPS is defined by theportions of the PPS which overlap with each of the reference spaces ofthe RPPS.
 9. A method according to claim 1, further comprising at leastone of: storing the PPS in a memory at the node; communicating the PPSto an end user; and displaying the PPS to the end user on a graphicaluser interface so that the PSS is viewable by the end user.
 10. A methodaccording to claim 1, wherein the space comprises: a two-dimensionalspace.
 11. A method according to claim 1, wherein the space comprises: athree-dimensional space.
 12. A node, comprising: a receiver designed toreceive position measurement information from a reference node; and aprocessor designed to generate, based on the position measurementinformation, a position probability space (PPS) which defines a spacethat encompasses possible positions where the node is possiblypositioned in the network.
 13. A node according to claim 12, wherein thePPS comprises: a centroid comprising a set of coordinates; and a set ofvectors which originate from the centroid and define the space aroundthe centroid, wherein a magnitude of each vector reflects the accuracyof the position in the direction of the vector.
 14. A node according toclaim 13, wherein the node includes a memory that stores a startingposition estimate comprising a starting centroid and a set of startingvectors, wherein the position measurement information defines a circlecentered at the location of the reference node and has a radius equal tothe distance between the node and the reference node, and wherein theprocessor is designed to determine, for each starting vector, whetherthat starting vector intersects the circle, and when the starting vectorintersects the circle, to reduce the magnitude of the starting vector toa distance between the starting centroid and an intersection point ofthe starting vector with the circle.
 15. A node according to claim 13,wherein the receiver is designed to receive updated position measurementinformation from the reference node, and wherein the processor isdesigned to generate, based on the updated position measurementinformation, an updated PPS (UPPS) by reducing the magnitudes of thevectors which define the PPS to reduce a space occupied by the UPPS incomparison to the space occupied by the PPS.
 16. A node according toclaim 13, wherein the processor is designed to re-center the centroid ofthe PPS such that it is substantially centered within the PPS when thecentroid of the PPS is not substantially centered within the space thatdefines the PPS.
 17. A node according to claim 13, wherein the receiveris further designed to receive first position measurement informationfrom a first reference node having a first fixed location and secondposition measurement information from a second reference node having asecond fixed location, wherein the first position measurementinformation is represented as first space centered at the first fixedlocation and having a first radius, and wherein the second positionmeasurement information is represented as a second space centered at thesecond fixed location and having a second radius, and wherein theprocessor is designed to generate an updated position probability space(UPPS) for the node by removing portions of any vectors of the PPS thatdo not overlap with both the first space and the second space such thatthe UPPS is defined by the overlapping portions of the PPS, the firstspace and the second space.
 18. A node according to claim 13, whereinone of the reference nodes comprises a mobile reference node having alocation specified by a reference position probability space (RPPS)associated with the mobile reference node, wherein the RPPS comprises areference centroid and a set of reference vectors associated with themobile reference node, wherein each of the reference vectors defines areference space, wherein each reference space comprises a referencecentroid that is centered at the end of the reference vector and has areference radius that originates from the reference centroid, andwherein the receiver is further designed to receive the RPPS, andwherein the processor is further designed to generate an updatedposition probability space (UPPS) for the node by removing portions ofany vectors of the PPS that do not overlap with at least one ofreference spaces such that the UPPS is defined by the portions of thePPS which overlap with each of the reference spaces of the RPPS.
 19. Anode according to claim 12, further comprising at least one of: a memorydesigned to store the PPS at the node; a transmitter designed tocommunicate the PPS to an end user; and a graphical user interfacedesigned to display the PPS to the end user so that the PSS is viewableby the end user.
 20. A node according to claim 12, wherein the spacecomprises: a two-dimensional space.
 21. A node according to claim 12,wherein the space comprises: a three-dimensional space.